Statement - 1 : When ultraviolet light is incident on a photocell , its stopping potential is `V_(0)` and the maximum kinetic energy of the photoelectrons is `K_(max)` when the ultraviolet light is replaces by X- rays both `V_(0) and K_(max)`increase
Statement - 2 : Photoelectrons are emitted with speeds ranging from zero to a maximum value became of the range of frequencies present in the incident light

Options

A. Statement-1 is true, Statement-2 is true, Statement-2 is the correct explanation of Statement-1.
B. Statement-1 is true, Statement-2 is true, Statement-2 is not the correct explanation of Statement-1.
C. Statement-1 is false, Statement-2 is true.
D. Statement-1 is true, Statement-2 is false.

Answer

To solve the question, we need to analyze both statements provided and understand the principles of the photoelectric effect.

### Step-by-Step Solution:

1. **Understanding Statement 1**:
- The statement mentions that when ultraviolet light is incident on a photocell, the stopping potential is \( V_0 \) and the maximum kinetic energy of the photoelectrons is \( K_{max} \).
- When this ultraviolet light is replaced by X-rays, both \( V_0 \) and \( K_{max} \) increase.

2. **Analyzing the Photoelectric Effect**:
- According to Einstein's photoelectric equation:
\[ E = \frac{hc}{\lambda} = \phi + K_{max} \]
where \( E \) is the energy of the incident photons, \( \phi \) is the work function of the metal, and \( K_{max} \) is the maximum kinetic energy of the emitted photoelectrons.
- When the wavelength decreases (as it does when moving from ultraviolet to X-rays), the energy \( E \) increases.

3. **Effect of Increasing Energy**:
- Since the work function \( \phi \) is constant for a given metal, an increase in the incident photon energy \( E \) results in an increase in \( K_{max} \):
\[ K_{max} = E - \phi \]
- Consequently, if \( K_{max} \) increases, then the stopping potential \( V_0 \) also increases, since:
\[ K_{max} = eV_0 \]
- Therefore, both \( V_0 \) and \( K_{max} \) increase when ultraviolet light is replaced by X-rays.

4. **Conclusion for Statement 1**:
- Statement 1 is **True**.

5. **Understanding Statement 2**:
- The statement claims that photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the incident light.
- In the context of the photoelectric effect, if the light has a single frequency, the emitted electrons will have a maximum kinetic energy determined by that frequency.

6. **Analyzing the Range of Speeds**:
- The range of speeds (or kinetic energies) of emitted photoelectrons does not arise from a range of frequencies, but rather from the varying energy losses due to collisions within the material.
- If an electron experiences collisions, it may lose kinetic energy, resulting in a speed less than the maximum. Thus, the maximum speed corresponds to electrons that do not lose energy through collisions.

7. **Conclusion for Statement 2**:
- Statement 2 is **False**.

### Final Verdict:
- Statement 1 is True, and Statement 2 is False.